Irent a gym for $150.00 for 30 students. another time i rent the gym for
@270.00 for 70 students. i need to find a fixed rate.

$60.

Step-by-step explanation:

Let x be the number of students and y be the total cost of renting the gym.

We are told that we rent a gym for $150.00 for 30 students. Another time we rent the gym for  $270.00 for 70 students.

To find the fixed rate let us write the equation of line representing the total cost of renting gym for x students.

We will write equation of the line representing total cost in slope-intercept form of equation.

, where,

m = Slope of the line,

b = y-intercept or initial value.

Let us find slope of our line using slope formula.

Upon substituting coordinates of our points (30,150) and (70,270) in slope formula we will get,

Therefore, the slope of our line is 3, which represents cost of using gym per student.

Let us substitute m=3 and coordinates of point (30,150) in slope-intercept form of equation.

So the equation represents the total cost of renting gym for x students.

As total cost of renting gym includes charges per student plus fixed rate. The cost of using gym per student is $3.

Since, y-intercept represents the initial value. Therefore, the fixed rate for the gym is $60.